- #1
Shackleford
- 1,656
- 2
Homework Statement
z ∈ ℂ
What is the radius of convergence of (n=0 to ∞) Σ anzn?
Homework Equations
I used the Cauchy-Hardamard Theorem and found the lim sup of the convergent subsequences.
[tex]a_n = \frac{n+(-1)^n}{n^2}[/tex]
limn→∞ |an|1/n
The Attempt at a Solution
I think that the radius of convergence is one, i.e. |z| < 1. I figured that the numerator would tend to n with the oscillating 1 and so you'd get [tex]\frac{n^{1/n}}{n^{2/n}} = 1[/tex]
R = 1/limn→∞ |an|1/n